Hedibert F. Lopes
ProfessorInsper Institute of Education and Research, Sao Paulo, Brazil
Bayesian Analysis in Latent Factor and Longitudinal Models
This thesis is a collection of studies in the field of multivariate Bayesian statistics. In the first part we concentrate on model uncertainty in factor models by proposing a novel reversible jump MCMC algorithm that accounts for model uncertainty directly in the model setting. For comparison we consider a variety of strategies to compute normalizing constants. We study briefly cases where little prior information is available and default analysis must take place. We end with some simulated examples and a real application. In the second part we use factor models to describe the covariance structure of time series, with special attention to financial time series where the factor variances have a multivariate stochastic volatility structure. We extend previous work by allowing the factor loadings, in the factor model structure, to have a time-varying structure. Simulation-based sequential analysis techniques are used in some real data applications, where predictive and financial performance are the main interest. In the third and final part of the thesis, we propose a new way of combining information from related studies. We extend traditional random effects models to random measure models by allowing parameters in the model to be partially described by a probability measure common to all studies, and partially by a probability measure that is specific to each study. Both measures, common and specific, are represented by mixtures of normals. First we consider a model where the numbers of components in the mixtures are fixed; then we extend the model to an encompassing model where the number of components are treated as random in a second stage, in which case a reversible jump MCMC algorithm is needed to assess the posterior probability for the competing models. The motivation comes from meta analysis over related cancer studies.